Want to feel like you’re on a desert island? Dramatic cliffs with not a soul in sight are the order of the day here, the southernmost point in Europe. While it doesn’t have a year-round restaurant, it does have its own radio station, Gavdos FM, which transmits from a hut with a tin roof. Gavdos is renowned for its free camping, with small fires and camping permitted on the beach. Don’t miss Agiannis beach, rated as the second-best beach in the world by National Geographic in 2013. There’s more wildlife here than people – including the endangered Mediterranean monk seal and sea turtles.

Dramatic cliffs with not a soul in sight are the order of the day in Gavdos, the southernmost point in Europe

Get there: British Airways flies to Heraklion and offers a seven-night break at the five-star Blue Palace. From there, take a ferry from Hora Sfakion, or Paleochora.

You may have heard of Milos without even knowing: the Venus de Milo was discovered here, in the village of Tripiti, in 1820. Milos itself feels a little like going to the moon: dazzling white cliffs jutting at peculiar angles and volcanic coastal rock formations lend the place an otherworldly feel. The volcano is still active, but that’s a good thing as it means that the island has hot springs that you can bathe in. Perhaps the best of its 80 beaches is Sarakiniko, with twisted white rocks sprawling into a sparkling blue sea. There’s more to see underground, too: Milos’s catacombs, a labyrinth below the island, which date back to around the 1st-5th century.

Le saviez-vous ?

Many of Milos’ beaches are scattered with gem-like pebbles and its catacombs are rumoured to be older than Rome’s famous underground system, dating back to the 1st century. You can get to Milos via Athens.

Story time

The island takes its name from the character Icarus in Greek mythology who is said to have fallen into the sea near the island. Look out for graffiti artworks of the winged hero on walls dotted around the port of Evdilos.

You’ll have to get used to a new way of life on Ikaria. Shops and restaurants have a relaxed attitude to opening hours, and the Ikarians can be found chatting and singing outside tavernas until the early hours. In the village of Raches, the streets only start getting busy after sun down. We should probably take a leaf out of Ikaria’s book: the island is listed as one of Earth’s five ‘Blue Zones’, where people live measurably longer lives. By day, hike over the rugged landscape – there are plenty of footpaths leading to waterfalls and rivers to go wild swimming in.

Get there: British Airways flies to Mykonos and offers a seven-night break at the four-star Theoxenia, from there, you can fly on to Ikaria.

Before you leave Mykonos… Visit Vioma Organic Farm & Vineyard for a wine tasting and an unforgettable lunch made with the farm’s fresh produce.

Thousands of years ago, dwarf elephants roamed wild on Tilos. You can check out their skeletons at the palaeontological museum in Megalo Chorio, the island’s capital, which is overlooked by the Knight’s Castle, a magnificent medieval fortress. Livadia, just a few miles away from here, is the port village and the island’s largest settlement. Hiking along the coastline is a must for botanists: there are more than 400 species of herbs and flowers on the island. And the rare birds, such as Bonelli’s Eagles and Eleonora’s Falcons, that call the island home will keep birdwatchers occupied.

Get there: British Airways flies to Kos and offers a seven-night break at the five-star Helona Resort. From there, catch one of the three weekly ferries to Tilos.

Before you leave Kos… Why not go sightseeing on horseback? Trek along the beach and to remote villages, and stop off for a swim.

Anafi is a walker’s paradise, but mainly because there’s actually only one road on the island and nowhere to rent a car. The island’s steep cliffs and hairpin walkways will certainly challenge even the most experienced hikers, but the island’s unusual terrain also keeps tourists at bay. By day you can snorkel in the shimmering blue sea, or visit the monks in the ancient Zoodochos Pigi Monastery with its picturesque spire.

Anafi is a walker’s paradise, but mainly because there’s actually only one road on the island and nowhere to rent a car

Get there: British Airways flies to Santorini and offers a seven-night break at the five-star Iconic Santorini. From there it’s a two-hour ferry ride to Anafi, which runs once a day, most days in high season.

Before you leave Santorini… For the best view of the – justifiably – world-famous Santorini sunset, head to the west of the island for a drink at Palia Kameni cocktail bar.

Symi is the place the Greek jet-set don’t want you to know about. It’s not cheap, as you’ll see from the dazzling-white super-yachts lined up in its port. Neoclassical buildings flank the harbour town of Yialos, and every building in the town has been listed. Yet Symi still has rustic charm. The winding cobbled pathways and herds of cattle in the streets make the island feel authentically Greek. It gained its wealth from sponge fishing, and you can still see the copper helmets used by divers on display in the town. Do visit the 18th-century Venetian monastery of the Archangel Michael Monastery in Panormitis, which has the highest Baroque bell tower in the world.

Get there: British Airways flies to Rhodes and offers a seven-night stay at Electra Palace. From Rhodes, catch the ferry to Symi. Ferries go at least twice a day from spring to autumn.

Before you leave Rhodes… If you have time to see Lindos, on the southeast of the island, as well as Rhodes Town, then don’t miss the chance to go snorkelling at the uncrowded St Paul’s Bay.